WHAT CAN WE DO IN PHILOSOPHY USING FREGE'S AND KRIPKE'S LOGICS

Since its publication in 1967, Jean van Heijenoort's paper, 'Logic as Calculus and Logic as Language' has become a classic in the historiography of modern logic. According to van Heijenoort, the contrast between the two conceptions of logic provides the key to many philosophical issues underlying the entire classical period of modern logic, the period from Frege's Begriffsschrift (1879) to the work of Herbrand, Gödel and Tarski in the late 1920s and early 1930. The present paper is a critical reflection on some aspects of van Heijenoort's thesis. I concentrate on the case of Frege and Russell and the claim that their philosophies of logic are marked through and through by acceptance of the universalist conception of logic, which is an integral part of the view of logic as language. Using the so-called 'Logocentric Predicament' (Henry M. Sheffer) as an illustration, I shall argue that the universalist conception does not have the consequences drawn from it by the van Heijenoort tradition. The crucial element here is that we draw a distinction between logic as a universal science and logic as a theory. According to both Frege and Russell, logic is first and foremost a universal science, which is concerned with the principles governing inferential transitions between propositions; but this in no way excludes the possibility of studying logic also as a theory, i.e., as an explicit formulation of (some) of these principles. Some aspects of this distinction will be discussed.

Manuscrito, 2004

Abstract Guillermo Rosado-Haddock: In this paper on Oswaldo Chateaubriand's book Logical Forms I, I am mostly concerned with the critical task of indicating some shortcomings and stressing my disagreements with the distinguished scholar. The most important shortcoming of the book is Chateaubriand's unfamiliarity with Husserl's views on logic and semantics, some of which anticipate views propounded by the former--e.g., the distinction between logical law and logical necessity--, whereas others are more subtle than Chateaubriand's views--e.g. Husserl's views on the referent of statements. One of the most important contributions of Chateaubriand's book is his analysis and rejection of all forms of the so-called "slingshot argument". On the other hand, I disagree with Chateaubriand's rendering of some of Frege's views, though some of these are very common among Frege scholars. Finally, I assess Chateaubriand's criticisms of Kripke's views as well as those of Tarski. I tend to agree with his criticism of Kripke, but disagree with his assessment of Tarskian semantics. Abstract response: In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the distinction between the notion of state of affairs and the more general notion of situation of affairs conceived as a common substratum for different states of affairs. After a few remarks about Church’s slingshot argument in §3, I discuss several objections that Guillermo raises to my interpretation of Frege (§4), to Kripke’s notion of rigid designator (§5) and to my objections to Tarski’s semantic conception of truth (§6).

Felsefe Arkivi - Archives of Philosophy

Having drawn the distinction between logic as a discipline and logic as organon, this short paper focuses on the latter, the purpose of which is twofold. First, it highlights the importance of second-order logic and modal logic in ontology. To this aim, the role of second-order logic is illustrated in formalizing realist ontology committing to the existence of properties. It is also emphasized how quantified modal logic helps clarify de re/de dicto distinction that implicitly takes place in ordinary language. Secondly, the paper concentrates on the significance of modal logic in the philosophy of language. In pursuing this goal, we considered Kripke's notions of rigid designator, necessary a posteriori and contingent a priori statements. Given the definition of rigid designator, it is possible to prove in quantified modal logic that an identity between proper names, like "Hesperus" and "Phosphorus", if true, is necessarily true. But the truth of the identity statement "Hesperus = Phosphorus" is known a posteriori. Therefore, there are necessary a posteriori truths. There are also contingent a priori true statements like "The length of stick S at time t 0 = one meter", as there exists a possible world in which this statement is false.

History and Philosophy of Logic, 2024

In many accounts of the history of logic, especially from the second half of the twentieth century and partly still today, Frege's rst book, Begri sschrift (1879), is singled out as the beginning of modern logic. In the English-speaking literature, this assessment goes back to the 1950s-60s when Frege's logical writings were rediscovered, after an initial period of neglect (although thinkers like Russell, Wittgenstein, and Carnap had paid close attention to it earlier). This is also the period during which modern logic consolidated itself, with its now standard sub elds: set theory, proof theory, model theory, and recursion theory. Good illustrations of this assessment of Frege's contributions can be found in William and Martha Kneale's book, The Development of Logic (1962), and in Jean van Heijenoort's revealingly entitled collection, From Frege to Gödel: A Source Book in Mathematical Logic. 1879-1931 (1967). The assessment was grounded in writings by a number of in uential logicians, including Alonzo Church, W.V.O. Quine, and Michael Dummett. Some of these writings, especially those by Dummett, include strong claims about how utterly original Frege's logical ideas were, thus representing a radical new beginning (cf. Reck 2023). Within the last 30-40 years such claims about the originality of Frege's views have been challenged and partly refuted in a number of ways. Thus, interpreters such as Christian Thiel, Gottfried Gabriel, Hans Sluga, etc. have pointed out the roots of some of Frege's logical ideas, including aspects of his logicist project, in neo-Kantian or post-Kantian philosophers like Hermann Lotze, J. F Herbart, and Wilhelm Windelband (cf. Gabriel 2002, Gabriel and, also the literature mentioned in them). Other interpreters of Frege, including Mark Wilson, Jamie Tappenden, and I, have discussed sources for Fregean ideas in mathematics, especially in nineteenth-century geometry, Bernhard Riemann's writings, and other works to which Frege was exposed in his mathematical education (cf. Tappenden 2008. Similarly, logical and mathematical in uences on Frege in works by Hermann and Robert Grassmann, Hermann Hankel, etc. may be worth exploring further, partly to clarify what Frege was reacting against (cf. Kreiser 2001). Yet another way in which the claim that modern logic started abruptly in 1879, with Begri sschrift, has been called into question is by rediscovering and highlighting earlier contributions by other logicians, such as George Boole, members of the Boolean school, as well as Bernard Bolzano (cf. Peckhaus 1997, Rusnock and. As this shows, it CONTACT Erich H. Reck

Michal Peliš (ed.) The Logica Yearbook 2007 (Prague: Filosofia), pp. 225-235, 2008.

The purpose of this paper is to examine the status of logic from a metaphysical point of view – what is logic grounded in and what is its relationship with metaphysics. There are three general lines that we can take. 1) Logic and metaphysics are not continuous, neither discipline has no bearing on the other one. This seems to be a rather popular approach, at least implicitly, as philosophers often skip the question altogether and go about their business, be it logic or metaphysics. However, it is not a particularly plausible view and it is very hard to maintain consistently, as we will see. 2) Logic is prior to metaphysics and has metaphysical implications. The extreme example of this kind of approach is the Dummettian one, according to which metaphysical questions are reducible to the question of which logic to adopt. 3) Metaphysics is prior to logic, and your logic should be compatible with your metaphysics. This approach suggests an answer to the question of what logic is grounded in, namely, metaphysics. Here I will defend the third option.

Synthese, 2023

Fichte's Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte's derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to correctly present the formal parts of Foundations. In this paper, however, we argue that Fichte's approach intuitively offers an important contribution to transcendental philosophy, and especially to philosophy of logic. We first point out the difficulties of Fichte's logic in the Foundations and improve it in a second part on the basis of a formal system in which both propositional logic and syllogistic are combined.

Bulletin of Symbolic Logic 19: 145-98, 2013

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Annals of Pure and Applied Logic, 2004

According to Frege's principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.

Logique et Analyse, 2021

In contemporary historical studies Peano is usually linked to the logical tradition pioneered by Frege. In this paper I question this association. Specifically, I claim that Frege and Peano developed significantly different conceptions of a logical calculus. First, I claim that while Frege put the systematisation of the notion of inference at the forefront of his construction of an axiomatic logical system, Peano modelled his early logical systems as mathematical calculi and did not really attempt to justify reasoning. Second, I argue that in later works on logic Peano advanced towards a deductive approach that was closer to Frege’s standpoint.

Principia: an international journal of epistemology, 2007

In this paper six of the most important issues in the philosophy of logic are examined from a standpoint that rejects the First Commandment of empiricist analytic philosophy, namely, Ockham's razor. Such a standpoint opens the door to the clarification of such fundamental issues and to possible new solutions to each of them. As an absolute principle, which is what it purports to be, Ockam's razor is the expression of a philosophical castration complex.